Question

A marketing organization wishes to study the effects of four sales methods on weekly sales of a product. The organization employs a randomized block design in which three salesman use each sales method. The results obtained are given in the following table, along with the Excel output of a randomized block ANOVA of these data.

	Salesman, j
Sales Method, i	A	B	C
1	40	31	28
2	43	29	23
3	33	22	19
4	32	19	17

ANOVA: Two-Factor without Replication
SUMMARY	Count	Sum	Average	Variance
Method 1	3	99	33.0000	39.0000
Method 2	3	95	31.6667	105.3333
Method 3	3	74	24.6667	54.3333
Method 4	3	68	22.6667	66.3333
Salesman A	4	148	37.00	28.6667
Salesman B	4	101	25.25	32.2500
Salesman C	4	87	21.75	23.5833

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Rows	234.0000	3	78.0000	24.00	.0010	4.7571
Columns	510.5000	2	255.2500	78.54	.0000	5.1433
Error	19.5000	6	3.25000
Total	764.0000	11

(a) Test the null hypothesis H₀ that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set α = .05. Can we conclude that the different sales methods have different effects on mean weekly sales?

F = 24.00, p-value = .0010;   (Click to select)   Do not reject   Reject   H₀: there is   (Click to select)   a difference   no difference   in effects of the sales methods (treatments) on mean weekly sales.

(b) Test the null hypothesis H₀ that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set α = .05. Can we conclude that the different salesmen have different effects on mean weekly sales?

F = 78.54, p-value = .0000;   (Click to select)   Reject   Do not reject   H₀: salesman   (Click to select)   do   do not  have an effect on sales

(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales method(s) maximize mean weekly sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Method 1 – Method 2:	[   ,  ]
Method 1 – Method 3:	[   ,  ]
Method 1 – Method 4:	[   ,  ]
Method 2 – Method 3:	[   ,  ]
Method 2 – Method 4:	[   ,  ]
Method 3 – Method 4:	[   ,  ]

Answer 1

a)  Reject   H0: there is    a difference    in effects of the sales methods

b)    Reject    H0: salesman    do  have an effect on sales

c) MSE =    3.2500
q-statistic value(0.05, 4, 6 ) = 4.8956

critical value = q*√(MSE/2*(1/ni+1/nj)) =5.10
confidence interval = mean difference ± critical value

count, ni =	3	3	3	3
mean , x̅ i =	33	31.6667	24.6667	22.66667

			confidence interval
population mean difference	critical value	lower limit	upper limit
µ1-µ2	1.33	5.09550	-3.76	6.43
µ1-µ3	8.33	5.10	3.24	13.43
µ1-µ4	10.33	5.10	5.24	15.43
µ2-µ3	7.00	5.10	1.90	12.10
µ2-µ4	9.00	5.10	3.90	14.10
µ3-µ4	2.00	5.10	-3.10	7.10